Mapping Dark-Matter Clusters via Physics-Guided Diffusion Models

Galaxy clusters are powerful probes of astrophysics and cosmology through gravitational lensing: their mass, dominated by 85% dark matter, distorts background light. Yet, mass reconstruction lacks the scalability and large-scale benchmarks to process the hundreds of thousands of clusters expected from forthcoming wide-field surveys. We introduce a fully automated method to reconstruct clustersurfacemassdensityfromphotometryandgravitationallensingobservables. Central to our approach is DARKCLUSTERS-15K, our new dataset of 15,000 mock cluster observations with paired mass and photometry maps, the largest to date, spanning multiple redshifts and simulation frameworks. We train a plug-and-play diffusion prior on DARKCLUSTERS-15K that learns the statistical relationship between mass and light, and draw approximate posterior samples constrained by weakand strong-lensing observables, yielding principled reconstructions with well-calibrated empirical uncertainties. Our approach requires no expert tuning, runs in minutes rather than hours, achieves higher accuracy, and matches experttuned reconstructions of the MACS 1206 cluster. We release our method and DARKCLUSTERS-15K to support upcoming wide-field cosmological surveys.